A Fallacious Aphorism: My enemy's enemy is my friend

Robleh Wais 5/26/18


The above statement you ve no doubt heard in your lifetime. Did you know it s an example of flawed reasoning? It might appear to be on solid ground at first glance. I believe it is modeled on an arbitrary principle in algebraic math that states the operation of multiplication on any two negative real numbers produces a positive real number. That is the non-technical description. We learn it in pre-algebra and never question it. We should challenge it. It s just a convention and not strictly speaking right. In fact, a Dutch mathematician did, Luitzen Brouwer, but this essay is not about that subject, so we won t digress to it. The allusion to this principle comes when we think of an enemy as a negative, then it would seemingly follow that enemy vs. enemy is friend, roughly speaking. Is this true? Stop to think that you can have many friends as well as enemies. Just because you and another person, share enemies, does not imply you and the other should be friends. It is in the realm of possibility that all three of you are enemies, for varying reasons. We'll look at this idea in depth.

First, we look at the positive interpretation of this idea. Suppose three of you are friends for different reasons. So, your various friendships are not of necessity connected to each other. You can be friends with one person because that person, perhaps uh, that person saved your life once. Then you could be friends with another because you are her lover, and friendship is necessarily a subset of a love relationship. Can you think of anybody that is in love, that is not simultaneously a friend of their lover? Add to that, you have a friend you met at a conference and found you share the same views and philosophic outlook and you consider him a like-minded colleague. You meet regularly to go to events and have intellectual discussions, play games together, etc. So, we have three friends of yours, presented and described. Add to this configuration that none of these three friends of yours know each other. Ask yourself should any of these friends consider themselves friends because they are friends of yours? If we apply the algebra of two positive make a positive, then any one of your friends should be mutual friends, right? Let's go further and suppose that two of these mutual friends of yours meet, that is, your girlfriend and your life-saving friend. The life-saving friend see your glamourous paramour and tries his best to woo her. She rebuffs him, especially since it was you that introduced them, and he uses this opportunity to betray you. She becomes his sworn enemy and tells you all about his underhanded behavior. He in turn, becomes her enemy. You however are unwilling to end your friendship with him because of this treachery, after all you in a sense owe him your life. You modify your relationship with him. You don t seek him out, and most of all keep him and your girlfriend apart, as it sows the seeds of enmity. We have two friends of yours, that are NOT friends of each other. This shows that friends of yours, are not necessarily friends of each other.

Second, we look at the negative interpretation of this idea. In this case we have you, your enemy, and someone who is an enemy of your enemy. Is it necessarily true that this last person must be your friend? That is the crux issue here. For this aphorism to attain the status of implicative truth, it must be the case that is always true. And even before we see an example, it might be clear to a reader that no such imperative truth is obtained. There are two necessary conditions we should observe with respect to this configuration. First, you know your enemy. Second, your enemy knows his/her enemy. But, you don t have to know your enemy s enemy. Nor, does your enemy s enemy have to know you. Thus, the relationship between you and your enemy s enemy is one of possibility not necessity. This means that you and your enemy s enemy could be friends but not because that person is inimical to your enemy. There is nothing in that relationship which implies necessity of friendship with you. This is crucial too. The hostility between yourself and another person does not serve to make you want to be friends with someone else that is hostile to that other person. Why not? The answer to this may seem complex, but really isn t. A negative relationship between yourself and another is no incentive for a positive relationship with someone else in such relationship with that person. Simply put, people don t become friends because of what they don t like, if even it s disliking the people the person they befriend dislikes. Three people can be enemies of each other for three different reasons none of which suffices to make them friends with one another. People become friends for positive reasons, not negative ones. The fact that your enemy has enemies in no shape, form or fashion implies that inimical party might be your friend. It is just a simple non sequitur. With that said, we don t even need to exemplify.

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